Problem: Solve for $x$ and $y$ using elimination. ${-6x+y = 3}$ ${5x-y = -4}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-6x+y = 3}\thinspace$ to find $y$ ${-6}{(1)}{ + y = 3}$ $-6+y = 3$ $-6{+6} + y = 3{+6}$ ${y = 9}$ You can also plug ${x = 1}$ into $\thinspace {5x-y = -4}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ - y = -4}$ ${y = 9}$